Equations (REF ) and (), and the analogous equations for \(g_\mathrm {R}\)  and \(g_\mathrm {I}\) , can be solved numerically for any value of \(|\lambda |\) , and for any choice of the initial condition \(p(x,t_0)\)  using, e.g., MATHEMATICA [1]}. The functions \(\psi (x,\lambda ,t)\)  and \(\chi (x,\lambda ,t)\) , can be thus obtained by using equations (REF ) and (REF ).
The target functions \(\phi (x,W,t)\)  and \(\varphi (x,Q,t)\)  can then be obtained
by taking the Fourier inverse transform, i.e. by inverting eqs. (REF ) and
(REF ), respectively. Also in this case the computation can be performed numerically.
